One side of the spoon acts as a concave mirror (the side you scoop up with), the other acts as a convex mirror. In a concave mirror, if the object lies is at a distance greater than F from the mirror, where F is the focal dist, then the image formed is real and inverted. In a convex mirror, the image is always virtual and upright and smaller. The spoon has a very small F and that’s why you see an inverted image on the concave side, and an upright smaller image on the convex side.

If you take your face very close to the concave side of the spoon, than you will see an upright and magnified image. That’s how shaving mirrors work. In a spoon it may be difficult to see.

Well so what? I think a person able to ask that question could understand a simple, ''the concave nature of the spoon acts as a mirror which flips an image at its focal point''. How deep of an answer is your friend looking for?